On Gaussian self-similar random fields on a 2-adic plane

The article describes a new type of Gaussian fields on a two-dimensional 2-adic space, invariant under the translation group and group of scaling transformations (self-similar random fields). Fields are characterized by quadratic characteristic functionals defined by homogeneous generalized functions on a 2-adic space. The properties of the proposed generalized homogeneous functions are investigated and the positive definiteness of the correlation functionals is proved.